Applicant Jon Doe responded to the Craigslist ad on Sunday and said he is coming in for an interview today between 4 and 5:30 p.m.

Should "he is" be replaced by "he would" to agree with "responded"?

But: John Doe says he is coming in ...
Correct?

Click to expand...

Applicant Jon Doe responded to the Craigslist ad on Sunday and said he is coming in for an interview today between 4 and 5:30 p.m.

Applicant Jon Doe responded to the Craigslist ad on Sunday and said he would be coming in for an interview today between 4 and 5:30 p.m.

The second construction leaves me with a feeling of incompleteness. The subjunctive needs its requisite qualification. ...and said he would be coming in for an interview today between 4 and 5:30 pm if he can find a ride.

Also, changing it to he would doesn't create any sort of agreement with responded. They are not tied one to the other by any verb agreement rules. The clause boundary created by the conjunction and is very strong, just this side of a full stop. Few things cross that boundary.

Applicant Jon Doe responded to the Craigslist ad on Sunday and said he is coming in for an interview today between 4 and 5:30 p.m.

Should "he is" be replaced by "he would" to agree with "responded"?

But: John Doe says he is coming in ...
Correct?

Click to expand...

I need more context. Is this dialogue ? A status report? Narrative in past tense story? Narrative in a present tense story?

I think that the unarguably correct version would have a tense change, yes:

Applicant Jon Doe responded to the Craigslist ad on Sunday and said that he would be coming in for an interview today between 4 and 5:30 p.m.

As dialogue, your choice of tense sounds perfectly natural:

"What about John Doe?"
"He called. He's coming in between 4 and 5:30."
Edited to babble on: This example is pretty complicated. It refers to three separate times:

Past: When called
Present: When the state of things is that he is planning to come in
Future: When he will actually come in

And it adds the casual use of "he is coming in" to mean, really, "he is planning on coming in" or "the present plan is that he will come in". So I think that your example requires a casual, dialogue-like voice, and the present tense of either a present tense story or of dialogue.